We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mix...We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model;in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.展开更多
The hippocampus has been extensively implicated in spatial navigation in rodents and more recently in bats.Numerous studies have revealed that various kinds of spatial information are encoded across hippocampal region...The hippocampus has been extensively implicated in spatial navigation in rodents and more recently in bats.Numerous studies have revealed that various kinds of spatial information are encoded across hippocampal regions.In contrast,investigations of spatial behavioral correlates in the primate hippocampus are scarce and have been mostly limited to head-restrained subjects during virtual navigation.However,recent advances made in freely-moving primates suggest marked differences in spatial representations from rodents,albeit some similarities.Here,we review empirical studies examining the neural correlates of spatial navigation in the primate(including human)hippocampus at the levels of local field potentials and single units.The lower frequency theta oscillations are often intermittent.Single neuron responses are highly mixed and task-dependent.We also discuss neuronal selectivity in the eye and head coordinates.Finally,we propose that future studies should focus on investigating both intrinsic and extrinsic population activity and examining spatial coding properties in large-scale hippocampal-neocortical networks across tasks.展开更多
Micro-mixing is an important mechanism, which works simultaneously with macro-mixing in chemical reactors in process industries, for achieving the best selectivity with respect to desired products. In about a half cen...Micro-mixing is an important mechanism, which works simultaneously with macro-mixing in chemical reactors in process industries, for achieving the best selectivity with respect to desired products. In about a half century, a huge amount of data and knowledge has been accumulated from theoretical and experimental studies on micromixing. Nevertheless, those results are mostly composites of simplified theoretical and empirical models, and the true nature of interactions of flow inhomogeneity and micro-mixing with chemical reaction has not been fully unveiled. This article reviews the progress in micro-mixing study in chemical reactors to date. A few important topics related to the nature, experimental evaluation, and numerical simulation of micro-mixing are addressed.Some suggestions are given hopefully to motivate more chemical engineers to devote their efforts to better understanding of micro-mixing in chemical reactors.展开更多
文摘We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model;in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.
基金supported by the National Science and Technology Innovation 2030 Major Program(2022ZD0205000)the Lingang Lab(LG202105-01-08).
文摘The hippocampus has been extensively implicated in spatial navigation in rodents and more recently in bats.Numerous studies have revealed that various kinds of spatial information are encoded across hippocampal regions.In contrast,investigations of spatial behavioral correlates in the primate hippocampus are scarce and have been mostly limited to head-restrained subjects during virtual navigation.However,recent advances made in freely-moving primates suggest marked differences in spatial representations from rodents,albeit some similarities.Here,we review empirical studies examining the neural correlates of spatial navigation in the primate(including human)hippocampus at the levels of local field potentials and single units.The lower frequency theta oscillations are often intermittent.Single neuron responses are highly mixed and task-dependent.We also discuss neuronal selectivity in the eye and head coordinates.Finally,we propose that future studies should focus on investigating both intrinsic and extrinsic population activity and examining spatial coding properties in large-scale hippocampal-neocortical networks across tasks.
基金Supported by the National Natural Science Foundation of China(21376243,91434126)National Key Research and Development Program(2016YFB0301702)+1 种基金the State Key Development Program for Basic Research of China(2012CB224806)Jiangsu National Synergetic Innovation Center for Advanced Materials
文摘Micro-mixing is an important mechanism, which works simultaneously with macro-mixing in chemical reactors in process industries, for achieving the best selectivity with respect to desired products. In about a half century, a huge amount of data and knowledge has been accumulated from theoretical and experimental studies on micromixing. Nevertheless, those results are mostly composites of simplified theoretical and empirical models, and the true nature of interactions of flow inhomogeneity and micro-mixing with chemical reaction has not been fully unveiled. This article reviews the progress in micro-mixing study in chemical reactors to date. A few important topics related to the nature, experimental evaluation, and numerical simulation of micro-mixing are addressed.Some suggestions are given hopefully to motivate more chemical engineers to devote their efforts to better understanding of micro-mixing in chemical reactors.
